I dont see why it wouldnt fit.
If anything you would need a new power supply in your computer to go with that 6770. If you get the 6770, you are going to need a new power supply, which will result in more money.
The 7750 would not require a power supply upgrade and would also fit.
Both should fit, but the 6770 should fit. I fit a 5770 (same card) in my cousin's Pavilion thats like yours.
Thanks for the info, I knew that I needed a new PSU, I just thought that was too obvious too mention. But then again this is a very open form... lol. I remember trying to fit a 6770 card in my case before and it wouldn't have enough space because the hard drive was in the way. I don't think the card would fit unless I moved my hard drive down a slot? Did the guy's computer that you installed the 5770 on have it's hard drive directly in front of the card or was it in a lowers slot? My pci-e goes straight through to my hdd bay for me